A semiparametric model for cluster data

Wenyang Zhang Jianqing Fan Yan Sun

Statistics Theory and Methods mathscidoc:1912.43335

Annals of statistics, 37, 2377, 2009.10
In the analysis of cluster data the regression coefficients are frequently assumed to be the same across all clusters. This hampers the ability to study the varying impacts of factors on each cluster. In this paper, a semiparametric model is introduced to account for varying impacts of factors over clusters by using cluster-level covariates. It achieves the parsimony of parametrization and allows the explorations of nonlinear interactions. The random effect in the semiparametric model accounts also for within cluster correlation. Local linear based estimation procedure is proposed for estimating functional coefficients, residual variance, and within cluster correlation matrix. The asymptotic properties of the proposed estimators are established and the method for constructing simultaneous confidence bands are proposed and studied. In addition, relevant hypothesis testing problems are addressed. Simulation studies are
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  title={A semiparametric model for cluster data},
  author={Wenyang Zhang, Jianqing Fan, and Yan Sun},
  booktitle={Annals of statistics},
Wenyang Zhang, Jianqing Fan, and Yan Sun. A semiparametric model for cluster data. 2009. Vol. 37. In Annals of statistics. pp.2377. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191221113759166622895.
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